The president still plays a significant role when it comes to economic policies. He chooses the heads of the secretary of treasury and has a lot of control over the federal reserve board. Despite not being able to take any direct action he still has a lot of pull.

Which probably had more to do with the fact that the modern world was basically being invented at the time than any political movements.
Also, in that timeframe, the two parties were in the process of switching platforms. Republicans of that era favored big government while Democrats favored small, for instance.